Question

Given: (∠ABC ≅ ∠DEF) and (∠GHI ≅ ∠DEF)
- Prove: (m∠ABC = m∠GHI)

Answer 1

Using the fact that ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF, we can apply the Transitive Property of Equality to show that m∠ABC equals m∠GHI because they are both equal to m∠DEF.

Step-by-step explanation:

The question provided involves the concept of congruent angles. In geometry, angles that are congruent have equal measures. This is represented by the symbol '≅', which you can see in the statement ∠ABC ≅ ∠DEF.

In addition, a second pair of congruent angles is given as ∠GHI ≅ ∠DEF. From these two statements, we can deduce that if m∠ABC = m∠DEF and also m∠GHI = m∠DEF, then by the Transitive Property of Equality, which states that if a = b and b = c, then a = c, it must be true that m∠ABC = m∠GHI.

This is a straightforward proof that requires an understanding of basic geometric principles. Here's a step-by-step approach to the proof:

1. Given that ∠ABC ≅ ∠DEF, we have m∠ABC = m∠DEF.
2. It is also given that ∠GHI ≅ ∠DEF, which means m∠GHI = m∠DEF.
3. By the Transitive Property of Equality (since m∠DEF is equal to both m∠ABC and m∠GHI), we can conclude that m∠ABC = m∠GHI.